A common scheme to detect signals, such as acoustic or electromagnetic radiation, is to deploy an array of sensors, and add their outputs coherently. Because noise is essentially random, and an informational signal is not, in a coherent sum the power from the signal adds cumulatively over the array, whereas the noise self cancels, increasing signal to noise for the array as a whole. A common expedient to beamforming is the cross-spectral density matrix. For an NxQ array of sensors, where N and Q are integers that are greater than zero and may equal 1 so long as both are not equal to one, the elements of this matrix are Z.sub.l Z.sub.m *, where Z.sub.1 is the complex output of the lth element of the array, and Z.sub.m * is the conjugate of the complex output of the mth element. Beamforming is then conveniently done using a steering vector S.sub.v, i.e.: EQU s(t)=(S.sub.v).sup.T MS.sub.v
where s(t) is the beamformed signal at time t, T indicates a transposed vector, and M is the cross-spectral density matrix. A typical set of elements for S.sub.v is W.sub.n e.sup.i.omega.(n-1).tau., where .omega. is the angular frequency of the signal, .tau. is the time of travel for the signal between consecutive elements in the array, i=(-1).sup.1/2, and W.sub.n a scalar associated with the nth array element, e.g. the gain of the element.
From this, it is plain that beamforming is a good approach to the detection of weak signals. Unfortunately, weak signals occur commonly in the presence of short-lived, large amplitude, noise, such as shot noise, or other forms of sensor self-noise, electric discharge in the vicinity of low amplitude electromagnetic communications, or surface waves or surface ships in the vicinity of submerged acoustic sources. One approach non-specific to beamformers has been to filter signals from a time series of detector outputs x.sub.1, . . . , x.sub.p according to the AWSUM.sub.z algorithm: ##EQU3## where z is a positive integer. See, U.S. application Ser. No. 08/314281,filed Sep 30, 1994 now abandoned and U.S. application Ser. No. 08/917964 filed Aug 27, 1997, now allowed. Because of the exponents, this is a sum of reciprocals, and only after the summation is the result re-inverted. As such, large amplitude fluctuations will have small reciprocals, and contribute little the summation. In this manner, the effect of these large noise excursions are filtered from the data. This approach, however, is incoherent in that it takes no account of the phase of the members of the time series. An attempt to do this is presented in U.S. Pat. No. 5,732,045 issued on Mar. 24, 1998 in which the real and imaginary portions of the time series are separately processed according to the above equation. However, an approach tailored to the specific problems of beamforming is needed. Hitherto, elements of the matrix have been filtered to an extent by taking data from the array at a series of times, forming the matrix for each time, and then averaging each value of the matrix over the times. As a practical matter this still leaves matrix elements susceptible to large noise fluctuations.